Not discouraging any other answers, but myself and others have tackled this question a couple times; see if any of these links can illuminate.
My interpretation is mostly based on Tonio Andrade's work, but I've also looked into Di Cosmo, Geoffrey Parker, Frederic Wakeman, and others; in the runup to the Opium Wars, where the Qing suffered their most devastating defeats, they hadn't fought a symmetric war in decades, if not centuries. The last major confrontation between the West and China came in the 1660s, when the Chinese had just come off a major arms race with the Manchus in the north, and ended with a Chinese victory over the Dutch. When they next clashed in 1839, the British had just come off the most intense military conflict in world history, while the Qing had been butchering nomads, pirates, rebels, and bogging down in Southeast Asian jungles trying to fight the Burmese and Vietnamese.
That said, there were important cultural reasons for the superior technology that enabled the British to destroy the Qing in the Opium Wars. The West had more advanced mathematics, the conventions of technical drawing that let them disseminate advanced technology more quickly, logical proofs dating back to Euclid, and so on. Being able to calculate projectile motion, the expansion rate of gunpowder, and tap into mineral energy let them build far superior weaponry.